© 2009 by Paul R. Bynum |
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Glossary |
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Absolute: Unchanging. The ultimate standard of evaluation or judgment for action. Age of Property: In real estate, reporting the chronological age, or the difference between the current year and the year built. Agent: A real estate professional trained to counsel and represent a client in the buying or selling of real estate. Agent Productivity: A real estate term used by companies to indicate the volume of sales, consistency, and average sale price of an agent working with the company. Volume of sales indicates their total market influence. Consistency indicates balanced and unwavering work habits. Average sale price indicates social strata of clients. A complete Agent Analysis includes these aspects and more. Amenities: The extra “perks” offered by a piece of property, beyond mere square-footage, or age. It would include such things as, drapes, sound wiring, central vacuum system, home theater, and many others. Appreciation: A gain in the value of property for any reason. Arithmetic Operations: Mathematical operations on numbers consisting of Addition, Subtraction, Multiplication and Division. Any Arithmetic operation performed on a point on he Rational Number Line will result in a point still on the line. Average: A statistical term meaning the central location of a data set. There are many types of averages. Real estate analysis uses mean and median extensively. See Also: Mean, Median, Mode, Weighted averages, and Central Location. Absorption: A term indicating how quickly the market removes, (or absorbs,) homes from the current listing pool. Another term meaning essentially the same thing is “Months of Inventory.” The formula is: current listings divided by sales or number of pending per month. Example: Grandville has 36 homes on the market in a given price range. Average sales over the last 3 months are 6 per month. So: 36/6= 6 months of inventory. Put in other words: given the average rate of recent sales, it will take the market about 6 months to clear out the existing inventory. Of course, such a figure is relative and indicative of a snapshot condition- not what will really happen. Homes will continue to come on the market during the six-month period, and some will not sell at all. Still, the figure is good for indicating the speed of the market - a simple measure for a “seller’s market” or a “buyer’s market”. Generally, an absorption figure between 5 and 6 months supply indicates a stable market -an advantage to neither the buyer nor the seller. A figure below 5 indicates a seller’s market, and the lower the figure, the more strongly the sellers market. A figure above 6 indicates a buyer’s market in a particular category. Again, the larger the absorption figure, the stronger the market. Assumptions: In any type of analysis, certain ideas are accepted as true without proof. These are called “Assumptions”. Example: in “time series analysis” we assume that a “raw data” graph can be composed of other component graphs. We develop a method for extracting these simpler graphs and assume they tell us something about the real world. The proof, of course is in the pudding. If we find them useful and predictable, we continue to use them. Axis: In a chart or graph, there are two lines of scale that are set at right angles to each other. The horizontal scale is called the “x” or independent axis. The vertical scale is called the “y” or the dependent axis. |
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Bonds: A Bond is a note due the
bond holder, usually in annual premiums or in one lump sum at the end of a
specified time period. Bond holders are creditors.
Builder: A generic term that generally means any person who is constructing new homes. See Also: Contractor, Developer Building Permits: Used to estimate the current population. From previous census, we used the average number of people per household figure. Knowing how many building permits have come on the market since the last population estimate, we use this and multiply it by the average per household. This gives an estimated increase of population. Building Sector: Applied to that area of the National Economy that tracks and analyzes new home construction. Bureau of Labor Statistics: A government agency that collects national data and analyzes it in different ways. They publish the “Consumers Price Index” every month as well as employment statistics. Business Cycles: A reoccurring pattern seen in the growth and decline of business activity. Although most economists agree there are cycles, it is not always clear when they start, end, or if the frequency of the cycle is consistent. The causes are also hotly debated. Sometimes historical data indicates a cycle clearly. Oftentimes it is a bit ambiguous. The general consensus gives 8-12 years for each cycle. Whenever raw data from long term real estate sales is subjected to “time series analysis” the “business cycle” will be one of the component graphs. Buyer: The future receiver of the deed in a real estate transaction. The person making an offer to purchase real estate. Buyer’s Market: A term referring to an advantage the buyer has in negotiating an offer. Buyer’s Market can refer to a general region, or a narrow category of the entire market. For the most part, a Buyer’s Market is the opposite of a seller’s market. Evaluating a buyer or seller’s market involves the following three elements: 1. How many homes that are listed in the given category will actually sell? (In a Buyer’s Market the lower the percentage, the stronger the Buyer’s Market.) 2. How fast are the homes selling? (The longer the “Days on Market” (DOM), the better for the buyer.) 3. What is the “sales to list price ratio?” (The lower the percentage, the better for the buyer.) All these elements can be combined in a general formula. The more independent the elements, the better the resulting formula. The result of the formula is a relative number and has no absolute standard by which to be measured. However, in time an index can be established and a maximum and minimum figure used to gage an existing market as either a Buyer or Seller’s Market. Buying Pattern: A curve showing the annual ebb and flow of monthly buying activity. See Also: Seasonal Index Buying Pool: A virtual collection of buyers representing the demand for a given category of listings at any given time. Buying the Listing: Appealing to the greed of a seller by offering to market a piece of property above what the buying pool interest indicates. |
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Category: Sometimes a data
set may contain so many data elements that it becomes useful
to divide the range of data into smaller groups called categories.
Example: rather than analyzing the entire number of home sales throughout a given year, we can divide the number of sales into monthly categories-allowing us more useful and summary information. See Also: Class Intervals. Cause: (Causal Factor). One event or factor is the cause of another, if it can be demonstrated that the first event is both a necessary and sufficient condition for the appearance of the second. Example: A supply of homes and demand by buyers are a necessary condition for the production of Sales Volume, but individually they are not sufficient. The interaction of the two, however, is a necessary and sufficient condition and therefore we can say that supply and demand produce (or cause) Sales Volume. See Also: Correlation, Interpretation Census: A collection of data using the entire population of interest. Central Location: (Central Tendency,
Example: [1,2,4,6,6,7,8,8,9,9,9,34,46, 58, 96] is a 15 element series. Its center of distribution could be considered as 20.2, (the Mean,) as 8, (the Median,) or as 9, (the Mode.) In Grandville, the mean for 2005 was $150,000, the median was $132,000 and the mode was $103,500. Chart: (See graph) Class Intervals: Dividing a continuous data set into specific regions or classifications and treating each new region as individual elements (class interval) for a new series. Example: given the data set of say, 200 data points each being a measure of days on market. All 200 points of the series, lined up by themselves may not be very useful. We can create a new series that give the frequency of occurrence between 5-day intervals starting with zero and continuing to the highest number. Thus, we would have 0-4 DOM, 5-9 DOM, etc. Our original 200 point series is reduced to just 20 and is more easily graphed and summarized. By such order, new relationships can be seen and established that may have gone unnoticed. Client: As opposed to Customer, used to denote the type of relationship established between an agent and either a buyer or seller in which Fiduciary Duties are assumed. Closing: In relation to statistics, the day property transfers and the contract is fully executed. See Also: DUC under DOM Column Chart: A chart that uses height of columns to indicate how different categories (usually on the “x” axis), rank in relation with each other. See Also: Graph, Line Graph Comparables: The previous sales used in a CMA, for arriving at a list price for a subject property. Comparative Market Analysis (CMA): Arriving at a list price for a piece of property by using past sale comparisons (comparables) and current market conditions. Compensations: Used in connection of developing a CMA. A term meaning that once a basic list price is found by examining previous sales, consideration must also be given to current market conditions, such as other homes in the area, the season, etc. Competition: Current homes on the market that buyers would perceive as being in the same pool of choices for making an offer. Component Graph: A simple graph that is considered part of a more complex (composite) graph. Example: a seasonal trend graph can be created and studied by itself, and yet shown to be an element of a raw data graph. Composite Graph: A graph assumed to consist of individual component graphs. Example: raw data graphs when subjected to “time series analysis” can reveal simper graphs, such as: trends, seasonal patterns, and business cycles. Concessions: Items given up or traded while negotiating a real estate contract. Concurrent Indicator: An indicator, designed to identify the current state of the National Economy. See Also: Indicator, Lagging Indicator, Leading Indicator, Economic Indicators Condition: The state if property with respect to repairs needed. Constant: An unchanging value. Also, in mathematics a symbol for any quantity that is part of an expression and never varies. Example: Constants are symbolized by letters: a, b, c…famous natural constants include: π (the ratio of the diameter of any circle to its circumference = 3.14…), e (the base of natural logarithms = 2.71…), and the speed of light: 186,283 miles per second. See Also: Variable, Expression, Equation Consumer Confidence Index: (CCI) An indicator used to analyze the economy by measuring the confidence displayed by the consumer toward future events. See Also: Economic Indicators Consumer Price Index: (CPI) An economic indicator used to measure inflation in the
Contingency: A condition, giving one party in a contract a termination option . Continuous: See “Number” Contract: In real estate, a binding agreement between a seller and a buyer specifying terms, and the closing date. Contractor: Generally applies to the overseer of a home construction project who may be involved in the actual physical labor, or act to hire specialty subcontractors who work together to complete a home. Correlation: In statistics a term indicating the dependence between two series of numbers-how much one series can be used to predict the other. See Also: Correlation Coefficient Correlation Coefficient: In statistics a term indicating the strength of relationship between two series of numbers. That is, how strongly can one series be used to predict the results of another? The value of the Correlation Coefficient is a continuous range from –1 , through 0 to +1. Zero indicates no correlation whatsoever. The closer the value is to –1 or +1, the stronger the relationship between the series, while –1 or + 1 would show an exact relationship and predictability. Example: The correlation coefficient between the regional series days on market and the series of sold prices for these homes is .971. This indicates an almost exact predictability of length of time on market and the sales price of the homes. We would expect this to be a general principle we could rely on in the future. Counter-offer: An offer initiated by the seller to the buyer. The action voids the offer from the buyer, who is now under no obligation to accept the sellers proposal. Current Market Conditions: Establishing real estate goals with respect to the forces acting on the existing marketplace. Forces could include such factors as: The number of buyers, seasonal considerations, interest rates, etc. Currents: The available number of listings on the market at any given time. Curve: In mathematics and statistics a curve is any line connecting a series of points. If the points are the result of an equation, they are called values. If they are a result of collecting numbers from the real world, they are called data points. The curve may be a straight line, or any series of slopes imaginable. It is relatively easy to find values for an equation and construct a graph. However, it is difficult to start with data points (gathered from the real world), and find a curve that fits all the points. Most often data points give a curve which no mathematical equation can duplicate. Part of the process of forecasting is establishing trend curves in the data points that approximate an equation of the data collection. See Also: “Time Series Analysis”. Customer: A relationship with either a buyer or seller in which dealings in good faith are assumed, but Fiduciary Duties are not owed to the party. See Also: Client, Fiduciary Duties Cycle: A repeated rising and falling pattern within the set of data points of a time series. Examples: are seasonal patterns and business cycles. |
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Dashboard (Real Estate Graphic): A series of charts and graphs that collectively convey the health or state of the real estate market. There is no standardized dashboard and every statistician has their own idea and style of a useful collection of graphics that make up the dashboard. Data: (Data Elements, Data Points) A collection of alpha or numeric elements used for descriptive or statistical analysis. See Also: Element Database: A collection of records, each record pertaining to a separate MLS entry. Each entry may contain various fields that describe aspects of a sale, a current listing, a withdrawal, or an expired. Example: A sale record may consist of the MLS number, the date of sale, the address of the property, and the sale price. A database could contain thousands of records dating back several years (called the date range of the database.) The domain of the database is the city, region, or area that all records share in common. Database Management: Collecting, updating, analyzing, presenting, and archiving MLS data within a database. Data Point: In a graph, the location of a particular element of a data set. Data Set: (Data Series) A group of related data elements under consideration. Example: out of ALL the students in a school (the population), I select those whose name begins with “B”. This becomes a data set for further investigation. Days-On-Market (DOM): An acronym for “Days on Market.” Usually a count of the days from listing to pending. There are other counts possible. Example: DUC is days under contract-a count from pending to closing. Deflated: (Deflator Index). A data set after the trend of the inflation line has been removed. The amount of Inflation is usually reported as an index with the years 1980-1982 as a standard. The data set under consideration is first reduced to an index graph, then the trend of the Inflation Index is used to remove Inflation influences. See Also: “Time Series Analysis.” Deflation: In general, the result of prices falling over a period of time. See Also: Inflation. Demand: The idea of supply and demand is central to any discussion of the exchange of goods and services. In relation to real estate, demand is the extent of the pool of ready, willing, and able buyers for a given category at any given moment. Demand can be increased for various reasons. Example: Population increase will create a general increase in demand. Example: Shifting employment opportunities can create a demand in a specific category. Example: Lower interest rates will drive buyers out of the rental market and increase the demand of the housing market. Demographics: Makeup of a population studies according to various categories such as: income levels, ethnic backgrounds, family size, etc. Dependent: In statistics, a term meaning a close relationship or correlation between two series of numbers-that is, one series can be use to predict the other. Def 2: In mathematics a term meaning that one value depends upon the value selected for the independent variable. Depreciation: The loss in value for any
reason. Depression: In the Business Cycle, where production and economic activity are at there lowest point. It is not really defined as a measurable point, but is more of a descriptive term indicating dismal times. Related conditions would be: high unemployment, tight money, stagnant economy, business contraction and anxious attitudes. See Also: Business Cycles, Recession, Economic Indicators, Gross Domestic Product Developer: An individual or group that buys raw land and develops it for various purposes. It may be a commercial or residential development. If residential, they are called Subdividers or Subdivision Developers. They prepare the land, survey it, draw up Platt Maps, get with the utility companies for establishing easements, and seek approval from city planners. They may be involved with the actual building of homes, or sell lots to builders and contractors. Deviation: A measure of distance from a given point to another point. Usually used to describe distances from a central location to other data points in the series. Detrended: In relation to a data set on a graph, the resulting values or data points once the trend has been removed. Directly Related: A series of pairs of numbers are directly related if an increase in one member of the pair results in a increase in the other member. Graphically, we say the data points of a curve are directly related, if an increase in value along the “x” axis results in an increase in value along the “y” axis. In a Scatter-Plot graph, the relationship may not be exact, but a regression line through the points would follow the above description. See Also: “Inversely Related” Discount Rate: A rate set by the Federal Reserve. It is the percentage rate charged to members of the Federal Reserve banks for borrowing money. Discrete: See “Number” Distribution: In statistical analysis, any set of related values described by the amount of data points, their frequency, skewness, spread, and: central location Dow Jones: An index used to measure the activity and health of the Stock Market. See Also: Economic Indicators Dwelling Units: Defined to be a space normally created for a single family to occupy. Can be a single-family residential home, a rental unit, or a multi-family apartment complex containing many single units. Dynamic Chart or Graph: A chart that must be constantly updated with the market . Its message is directly related to current market conditions. See Also: Static Chart or Graph |
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Easement: Having an irrevocable right to the use of a land owner’s property. Economic Indicators: A gathered and tracked series of number used for clarifying, informing, or predicting some aspect of the economy. Examples: Common economic indicators include: The Gross Domestic Product, the unemployment rate, the Stock Market Indexes, and the Consumer’s Price Index. There are many more. Economics: The study of the production and distribution of goods and services. See also:Local Economy and National Economy Economist: One who studies Economics. Element: One component, piece or part of a whole. Example: Customer service is an element of agent success. Equation: A mathematical expression showing a relationship between two or more variables. Equations always include an equal sign (=) balancing two sides of the expression. The terms of the right side of the equal sign are equivalent to those on the left side. Example: a simple two-variable equation might be: Y = 2X. if we change the value of X (called the independent variable), the value of Y (the dependent variable) can be determined. If X=1,2,3… then Y =2,4,6… and so forth. If we place corresponding pairs of values on a piece of paper that has reference lines (called an axis) of X and Y, we create a graph of the equation. Employment: See unemployment Environment: In relation to homes, the current market conditions affecting the sale of the property. See Also: Heredity Error: Usually used to indicate an incorrect procedure in statistical analysis. Errors can be broken down into various categories. Existing: A term to distinguish homes having a previous occupant from those without. See Also: New Construction. Expired: Properties on the MLS that have reached the end of the listing period without selling. Exponential: A type of curve in which the independent variable is an exponent. Multiplying a number by itself (like 3x3), is called raising the number to the 2nd power. Mathematical shorthand would say: 32 . In this type of term, 3 is called the base and 2 is called the exponent. Thus 53=(5x5x5)=125, (Called 5 raised to the 3rd power). Again, 5 is the base and 3 is the exponent. Now if the independent variable X is an exponent, we have an exponential equation and the graph is called an exponential curve. Example: For Y=2X, 2 is the base and X (the independent variable) is the exponent. If we select X=1,2,3… then the values of the dependent variable Y becomes 2,4,8… The graphed curve is not a straight line but a curve with a steeply increasing slope. In many applications when dealing with population growth, exponential equations use the base “e”. The number e is a mathematical constant whose value begins: 2.718…and is called the base of natural of logarithms. The equation Y=eX can be used to show the change in population growth. If X represents different periods of time, then the equation indicates an accelerating increase in population as X (time) increases. We commonly say: population growth is exponential. Expression: In mathematics a word meaning any sentence or collection of symbols that are quantitatively related. The symbols consists of variables (x,y,z…), constants (a,b,c…), operatives (+ , -, …), and other symbols for clarifying the relationship ( (), [], S…). An expression may or may not be an equation or formula. Example: (X + Y) /2 is an expression that is neither an equation nor formula. |
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Federal
Reserve System (The Fed): An
agency of the
Forecasting: Statistical forecasting: Using past statistical data to predict future trends or events. Judgmental forecasting makes allowances for experience, intuition and hunches. Most forecasts are a combination of both types. (See Jinxed). Formula: In mathematics a formula is an expression of terms used to find a particular unknown. Usually the term formula is reserved for finding unknowns that are needed and used often in real world applications. Example: the formula for finding the annual interest paid on a loan is: I=PxR where I is the amount of interest paid, P is the principle amount invested, and R is the annual interest rate expressed as a proportion. Thus if P=$95,000 and R=.06 (6%) then I=$95,000 x .06 = $5,700 See Also: Equation Frequency: A measure of how often an event occurs in a series. A frequency graph (also called a histogram,) shows the frequency with which data elements or class intervals occur in a set of data elements. FSBO: A “For
Fiduciary Duties: The legal duties assumed when working with a Client in real estate. They Include: Obedience, Loyalty, Disclosure, Care, and Accountability. |
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Geometric Mean: Another measurement of average, central location, or midpoint. The geometric mean is used for data that is growing. It is found by multiplying the data points together and taking the root of the result using an index which corresponds to the number of data points. Example: [2,4,8] Multiplying them together gives 64 and taking the 3rd root gives 4, the Geometric Mean. Graph: A visual display relating independent and dependent variables. To plot a series of data points in relationship to time or some other category and give a visual interpretation of the relationship of the numbers. Improved information and insights are possible using various graphing techniques, that are not readily available by studying the numbers by themselves. See Also: Column Chart Line Graph Gross Domestic Product (GDP): The
king of all indicators for clarifying the extent and direction of the
See Also: Economic Indicators Growth Trend: In mathematics a growth trend is a curve that follows the data points indicating an increase over time. We may say the growth trend is the best-fit slope of the data point curve (usually estimated). Example: In studying population increase we look for the growth trend. This enables us to forecast the future population. See Also: Exponential, Population Growth, Population Studies |
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Heredity: In relation to a home, its structure, age, condition and style. Histogram: A graph showing the frequency with which data elements or class intervals occur in a set of data. Home Inspection: Usually made a contingency in a contract, giving the buyer the right to inspect and if necessary, reject the property. Home Warranty: An insurance policy for the buyer, insuring them against loss usually during the first year of ownership. |
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Independent: Use is statistical analysis to indicate the relative isolation or non-correlation one series of numbers have from other series. Def 2: The independent variable is also the one chosen, measured, or is arbitrary (within a range of values), from which the dependent variable can be calculated from a mathematical relationship or equation. Example: The series of the number of birds vs. the number of flying insects in a given region may have a strong relationship-that is we can use one series to predict the other series. In this case, the two series are dependent on each other. However, the number of birds vs. the number of rocks probably has no relationship whatsoever, and such series would be independent of each other. See Also: Dependent, Expression, Equation Index: In a relative numerical series, the establishment of a standard of reference as the number one, by dividing all numbers of the series by the smallest number. Example: 2,5,7,9,11,12,14 divide all by 2 gives: 1, 2.5, 3.5, 5.5, 6, 7. Useful in comparing two series of numbers graphically. Both series can be reduced to an index with the number 1 being the least, and both series then graphed on the same y-axis. Two series of numbers can also be indexed by dividing corresponding data points of one by the other. This has the effect of “removing” the dividing curve from the second curve and establishing the dividing curve as the base line (Horizontal line with Y=1). Useful in removing trend lines from a given curve. Example: Say the following is a series of data points representing annual growth of unit sales of residential homes in a given category: 45,50,52,55,57,60,63,66,70,73, and 77. Graphing this series produces a curve with an upward trend. If we now establish the equation for this trend (either by statistical methods or by “eye”), we can generate a second curve of the trend line by itself. Values of this series might be: 44, 47,50,55,58,61,64,67,70,73, and 76. Taking the trend line as our standard, and dividing each data point of the first curve by the data points of the trend curve gives a third series (a curve in which the first series is indexed to the second): 1.028, 1.013, 1.001, .993, .988, .986, .986, .989, .993, 1.000, 1.008, and 1.018. Graphing this new series gives a curve in proportion to the trend curve. Effectively, the new curve is the growth curve without the trend. We have “removed it”. If desired, we can analyze the remaining curve further. See Also: Growth Trend, Time Series Analysis Indicators: In general, an indicator is a series of tracked numbers that relate to the status of an economic condition. Example: the variation of Days on Market (DOM) relates to the presence and extent of a seller’s or buyer’s market. DOM could therefore be considered an indicator of a seller’s or buyer’s market. Indicators are not perfect. Some conditions, such as a seller or buyer’s market may take more than one indicators to achieve predictability. See also: Economic Indicators Leading Indicator Concurrent Indicator Lagging Indicator Inflation: Used as an economic indicator. A measure of increase of general prices of goods. Integers: The series of both positive and negative counting numbers, including zero. See also: “Number" Interest Rates: An indicator of economic health both locally and nationally. Interest is defined to be a percentage of an amount of money either borrowed or loaned. If borrowed, the interest defined by the interest rate is the cost of borrowing money. If loaned, the interest is the profit made. In real estate, low interest rates translate into low monthly house payments. Low interest rates tend to drive tenants out of the rental market and into home ownership. Conversely, high rates are good for the rental market. Interest rates frequently follow changes in the discount rate. While low rates are usually good for the real estate market, they do not infallibly predict more buyers. Interpretation: Analyzing events, charts or graphs, for causal as opposed to correlation factors. Inventory: In real estate, the inventory is the actual property for sale. Inventory and supply are therefore equivalent. Statistics finds it useful to track both existing and new construction inventory. Inversely Related: A series of pairs of numbers are inversely related if an increase in one member of the pair results in a decrease in the other member. Graphically, we say the data points of a curve are inversely related, if an increase in value along the “x” axis results in an decrease in value along the “y” axis. In a Scatter-Plot graph, the relationship may not be exact, but a regression line through the points would follow the above description. See Also: “Directly Related” |
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Jinxed: What your peers think of your future work after witnessing the results of your current forecast. |
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Kurtosis: A measure of the “flatness” of a normal distribution curve. |
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Lagging Indicator: An indicator, designed to confirm an established recent change in the National Economy. See Also:Indicator, Concurrent Indicator, Leading Indicator, Economic Indicators Leading Indicator: An indicator, designed to foretell the changing of the National Economy. See Also: Indicator, Concurrent Indicator, Lagging Indicator, Economic Indicators Line Graph: A type of chart where the data points are connected by a continuous curve. Used mainly when the data on the horizontal axis is continuous. It implies that a value can be interpolated between any two points on the curve. See Also: Column Chart, Graph Linear: A relationship between any two data points of a series of numbers that is constant is called Linear. If the data points were plotted and connected, they would form a straight line. Example: Consider the series of numbers: 3,6,9,12,15… The difference between any two numbers is three. Therefore this is a linear relationship, and would show a straight line (unchanging slope), if plotted on a graph. See Also: Graph, Logarithms, Scale, Slope List to
Listing: A piece of property being offered for sale and currently marketed by a real estate firm and available on the MLS. Listing Pool: The amount of inventory of homes on the market at any given time. Local Economy: The study of economics, (Labor, inflation, production, etc), in a given region. A local economy may or may not reflect the national economy. See Also: National Economy Location: Prime consideration of value of property. Logarithms: (Logarithmic). A logarithm is an exponent of a base in a mathematical expression. Example: in the expression Y=10X, Y is the dependent variable, X is the independent variable, and 10 is the base. X is called the exponent of 10. If we know that Y = 1000 for example, then 1000=10X would translate: to what power must 10 be raised to give 1000? Answer: 3 (10 x 10 x 10 = 1000). So the formal definition of a logarithm is: the number that must be assigned to the exponent to raise a given base to a given number. Logarithms have two standard bases. Ten base logarithms are called common logarithms, and base e logarithms are called natural logarithms. Base e logarithms are used to predict population growth and in financial formulas. Base 10 logarithms can be used as the reference axis in a graph. Example: Graphs having a wide ranging dependent variable, (Say Y has a range from 3-450), would be hard to read on a standard linear Y axis. By converting the numbers to logarithms (with base 10 say), we could reduce the height of the graph and still maintain relationships between the data points. By its nature, a logarithmic graph is a percentage increase graph. Low-ball Offer: An offer given by a buyer that is well below market value. Usually the buyer is hoping the seller has a desperate need to sell. |
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Magnitude: The size of a number without regard to direction or being positive or negative. Example: both –11 and +11 have a magnitude of 11. Market Activity Index (MAI): A measure of the “briskness”, momentum, or rate of change of the real estate market. See Also: Seller’s Market, Buyer’s Market Market Share: A business term indicating the percentage part in relationship to the whole. Example: We say that “Wonderful” company has a 15% market share in relationship to the total Inventory. In other words 15 out of 100 homes (3 out of 20) are listed by “Mr. Wonderful” and his company. Marketing: Exposing a product (or service) to a target audience with the purpose of convincing them to use the product. Marketing Time: Seen as the amount of time from list date to accepted contract, needed to sell a home. Marketing Plan: An in-place system, for getting a home sold Mathematics: The study of the general relationships among numbers. Mean: The most commonly understood average. The mean is found by adding together all the numbers in a data set and dividing by the count of data points. Example: [3,5,8,10,13,17]. Add the data set=56, divide by the amount of data points=6, answer=9.33 is the mean rounded to two decimal places. Rationale: In finding the mean, we are interested in the magnitude of the individual numbers, which we can interpret as distances. If we consider the series on a number line, and we add up all the distances above the mean to the other data points, it will equal the addition of the distances below the mean. Thus in the above series, (17-9.33)+(13-9.33)+(10-9.33)=(9.33-8)+(9.33-5)+(9.33-3)=12. The Mean can also be interpreted as the “center of mass” In other words, if the numbers represented 1 pound weights at the given distances from the end of a stick (3 inches, 5 inches, 8 inches, etc,) the mean would be that point on the stick where you could put your finger and the stick would balance. Uses: to find a central location where the sum of the deviations from that point in either direction is the same, we would want the mean. See Also: Central Location Median: A type of central location or average. The median is the middle number in a series of data points or elements. If the series contains an odd amount of elements, there is an exact midpoint. If the series contains an even amount of elements, the median is found by adding the two middle numbers and dividing by two. Example: [3,5,8,10,13,17]. Since there is an even amount of data points, the median is found by adding the mid two numbers in the series and dividing by two=(8+10)/2=9. Example: [3,5,8,10,13,17,20]. An odd amount of data points gives an exact midpoint=10 the median. Rationale: In establishing the median of a series we are interested in the amount of data points lying above and below the point. The deviation from the median is not important-as in the mean, but rather, amount of data points above and below the median establishes the point. Uses: A practical average more often than the mean-especially if the mean shows a great amount of skewness. A distribution of data points with a large amount of high values compared with low values will result in a mean average above the median. Suppose we use the mean to indicate the central tendency of sale prices of homes. If there were a few sales of very expensive homes, this could show an average price well above the median. If we indicate the central tendency by the median, we are saying that as many homes sold above this amount as below, or as many buyers bought homes above this amount as bought below. Meeting of the Minds: A term meaning the final acceptance by both the seller and the buyer of all the concessions made in a contract negotiation.
See Also: Economic Indicators MLS: The multiple listing service in a given region. Cooperating brokers join the local MLS and agree to share in the commission of the transaction. For statistical purposes, the MLS collects real estate data (or facilitates its collection.) From this massive database of current listings, historical sales, withdrawals, and expires in all cities and property types, we can run analysis and see trends. Mode: A type of central location or average. The mode is a number giving the amount of the most frequently appearing numbers in a data series. Example: [1,2,2,3,44,555,66,77,8,9]. The mode of the series would be 5. It is possible that a unique series lacks a mode. Rationale: In establishing the mode, we are most interested in the frequency or number of occurrences of a particular data point in a series. Consider all the sales of residential homes in NW Arkansas for 2004. Say there were 56 that sold for $103,500. If this were the figure with the highest amount of sales, then 56 would be the mode for the series. Momentum: A measure of the force of the market that keeps it on a trend without slowing down or taking a new direction. Resistance of the market to change. Months of Inventory: (MOI) See Absorption Figures Moving Averages: In time series analysis, finding the average of a series by using both past and future data points. Example: Given the DOM of 12 months worth of sales as: [30, 45,32,43,53,67,55,49,63,59,69,71]. Say we want to graph the points. But rather than graph the actual data points we decide to graph a 5 month moving average to help smooth out the monthly fluctuations to better indicate the trend K. In this case, we would start with number 32 and add the previous two months and the next two months. (Obviously such moving averages use historical data.) So our first point would be: 30 + 45 +32 + 43+ 53 = 40.6. Next, we would drop the earliest month value and add the next value of the series: 45 + 32 + 43 +53 + 67 = 48. Continuing this pattern would generate the 5 month centered moving average for this series: [40.6, 48, 50, 53.4, 57.4, 58.6, 59, 62.2]. Here, the trend is easier to see and graphs a smoother curve. See Also: Central Location |
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National Economy: Considering the economic state and influence of the entire nation as compared to the Local Economy, which only deals with factors affecting the immediate area. Negotiations: In a contract the act of giving, taking and trading before acceptance, given that both parties have there own wants desires, and needs. Good negotiations leave both parties satisfied with the compromises. Net Proceeds of Sale: The net amount due the seller of real estate when all commissions, fees and costs are deducted. See Also: Walk-away Price New Construction: Homes that have never been lived in. They fall into two categories: those that are being built on speculation of finding a buyer, (spec home,) and those being built with a buyer already obligated to the home, (Custom home.) New Home Starts: A monthly (sometimes quarterly,) measure of the quantity of homes breaking ground and under construction. Normal Distribution: Used in descriptive statistics to describe a series of numbers the graph of which follow a normal curve-that is-the mean, median, and mode of the series are identical. See Also: Distribution Northwest
Arkansas: For statistical purposes, the
combination of
Number: The attribute of quantity between objects. If there is a one-to-one correspondence between two classes of objects they are said to share the same number between them. Numbers can be ordinal: (first, second, third…,) counting: (1,2,3…,) rational (expressed as the ratio of two counting numbers,) real (a number that is the root of an algebraic equation with rational coefficients,) imaginary: (having the square root of a -1 as a factor,) and transcendental: (NOT the root of an algebraic equation with rational coefficients.) The interval between any given numbers can either be discrete (consists of counting numbers) or continuous (every conceivable location corresponds to a number.) The idea of abstract number beyond simple counting to say 4 or 5, is a late development in the evolutionary process Example: Discrete: 2,3,4,5 Continuous: an infinitely repeating decimal 1.6666…. |
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Offer: A proposal usually given by a buyer to a seller spelling out the terms and conditions under which the buyer will purchase the property. Not a contract until accepted by the seller Offer and Acceptance: The common name for a real estate contract. The way of presenting the offer to a seller can make or break a transaction. Off-Market Date: Off market date is the date a listing is removed from the market and is no longer current. This includes pending date, expire date and withdrawn date. Outliners: Data points in a data set that are abnormally distant from the mean. Outliners have a large affect on the mean of the series, and could (but not always,) indicate spurious data points. Overpriced: A term indicating a listing is
priced higher than the demand of the market would indicate. |
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Parameter: Characteristics or facts about a given population. [See also: statistic] Pattern: A re-occurring series of numbers, or a repeated theme in a collection of data points. The data points can be alpha-numeric, pictures, or any visual display. Peak: In relation to a graph, a high point. Not necessarily The
See Also: Business Cycles, Depression, Economic Indicators, Gross Domestic Product, Recession, Trough Pending: A listing not yet closed but has a signed contract. Also known as “under contract.” Pre-Approved Buyer: Accurately described as a buyer who has submitted all documentation to a lender, a credit check has been run on the buyer, all documents have been processed, and loan approval given. Awaiting for one last item: the home appraisal. Percentage: Comparing a numerical part to a whole. The larger number is divided into the smaller number. The result will be a decimal, which when multiplied by 100 and the percent sign added, gives the percentage. A percentage can be considered a ratio of the number compared to 100. Percentages lie between 0 and 100%- the 100% indicates the part IS the whole. Perception: In real estate, meaning as seen by a seller or buyer. A subjective evaluation (of say, an agent) that may or may not align with the truth. Personal Data: The use of an agent’s sales and listing data, to construct charts and graphs. Comparing these to the general market charts and demonstrate an agent’s superiority over the market (and by implication, other agents). Preliminary Title Report (Prelim): An initial report issued by a Title company, showing the owner of record, and the outstanding liens on the property. A good idea for an agent, is to have one issued as soon as the home is listed. See Also: Title Company Presentation: A visual method of presenting your services, facts, and resources to a prospective client or customer to motivate them to use your services. May include graphics, charts, visuals, or photographs. Has a “flow” containing a beginning, middle and end, and is centered around the needs of the client/customer. Plot: As a verb, to plot is to make a drawing (or chart), of data points using two scales. One scale is horizontal (called the “x” axis), and the other is vertical (called the “y” axis). As a noun, a Plot is the actual finished chart. See Also: Graph Population: The entire set of data points possible for a given study. Querying the entire population is called a “Census”. Usually a collected sample of a population is used to infer facts about the entire population. Population Growth: Having to do with the growth of a region. In real world terms: the rate of increase in the population is directly related to the size of the population. This sounds simple and obvious but leads to some extraordinary results. See Also: Demographics, Population Studies: Tracking the general trend and influx of people into the region. Can be combined with demographics. Predict: See Forecasting Price: Price is historical in character-a definite, obtained amount. Contrast it with value, which is speculatively in nature- a hoped for amount. Price Per SF: A common indicator of market value of a home. Finding the average price per square foot of a price category and city can be used to predict homes in the same area and price range. Price Range or Category: Dividing a series of home values into groups. Each group is continuous with no overlaps. The division can be quite arbitrary, or the series can be divided by “Buyer Percentiles” See Also: Category Price Reduction: A lowering of the list price from the original. Prime Indicators: National or Local Indicators that are frequently used due to their reliability and predictability. Profit-taking: A term meaning a seller is satisfied with the gain achieved in holding property and therefore sells it to realize a profit. Property: A general term for any piece of real estate. Proportion: Comparing a numerical part to a whole. When dividing a larger number into the smaller number, the result will be a decimal giving a proportion. This proportion can be considered a ratio of the number compared to 1. Percents lie between 0 and 1- the 1 indicates the part IS the whole. Example: Dividing 1 by 4 gives the proportion: .25 See Also: Percentage, Index Prospecting: A term meaning to actively and consistently seek people having a real estate need. Pythagoras: A Greek Philosopher from the 6-century B.C. Started a secret brotherhood teaching that numbers have a mystical meaning in and of themselves. |
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Random: In general it means unpredictable but with certain qualifications. Example: A truly random spread of data points when plotted on a graph (assuming a graph with infinite axis) would have the unique and interesting attribute of having no pattern or slope whatsoever. A line of any slope and extended to any length would divide the space into two regions-both of which would contain the same number of data points. Put another way, any curve of any slope could just as well serve as the slope of the random scattering. Neither would there be a maximum or minimum value of a data point. Example: Often times in statistics we generate what is called a random series of numbers. When the entire series is graphed it may indeed show a pattern or the values fall within certain prescribed limits. We may want to generate a random series that is normally distributed for a simulation experiment. Even thought the mean, median, and mode can be constructed before the series is generated, many different data sets containing unique data point values can give the same normal distribution. In this sense, our generated series would be called random. Range: A measure of variability in a data set. The smallest value of the data set subtracted from the largest value gives a measure of range. Range of Value: Meaning the value of a home is not intrinsic and should be considered as having a high and low figure for selling within a specified time- frame depending upon current market conditions. Rate of Change: Comparing changes month to month of an indicator in the real estate market. Ratio: Used in comparing numbers. Can be as simple as comparing a part to a whole. Comparing a part to a whole creates a fraction by placing the part in the numerator and the whole in the denominator. Example: If 6 homes out of 18 sales had 1 bathroom, we could say the ratio of 1 bath homes to all homes is: 6/18 . If there is a number that can evenly divide both the numerator and the denominator then our ratio can be reduced to an equivalent ratio. Example 6/18=(6/3)/(18/3)=1/3. We therefore say both fractions are in the same ratio, namely 1:3. Raw Data: Data as collected in the field before being cleaned, checked for errors, Seasonally Adjusted or analyzed. See Also: Seasonal Index and Seasonal Trends Real Estate: In general, Land and all improvements. Land is the core element. Without it we have personal property. Real Estate Market: A virtual location where sellers and buyers and/or their representatives gather to sell, buy, and otherwise negotiate for the exchange of real estate. Recession: A descriptive point reached in a Business Cycle. A recession is usually indicated when there has been three quarters of decreasing growth in the Gross Domestic Product. See Also: Business Cycles, Depression, Economic Indicators, Gross Domestic Product Recovery: A point in the Business Cycle when the trough is passed, and increased growth begins. See Also: Business Cycles, Depression, Economic Indicators, Gross Domestic Product, Recession Region: An area under discussion.
For our purposes,
Regional Planning: An agency devoted to planning and monitoring traffic flows, and population increases for a particular region. Relationship: Meaning one event (such as a data point in statistics,) can be used to explain another, or they occur together, or one follows another. Relationships do not necessarily mean one causes the other. They both could be caused by a third event. See Also: Correlation Relative
Number: A number that has no standard of reference or context for comparison. Rental Market: A virtual location where landlords and tenants and/or their representatives gather to rent, lease or otherwise negotiate for occupying real estate. Recession: A low point in the Business Cycle. Usually applied to the National Economy after two consecutive quarterly slow-downs of the GDP. Residential: Properties built for the purpose of dwelling units. Residuals: A random scattering of data points left after a composite graph has been broken down into all of its component graphs. See Also: Time Series Analysis |
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Sales to List Price Ratio: A measure of how close to list price the sale of property comes. Usually a simple percentage ratio: SP/LP*100%. Percentages of 100 indicate full-price offers. National averages are 94%-98%. Sales to Listings Ratio: A measure of how many homes coming on the market actually sell. Since only about 10% of the market is left after a year, the reported percentages are for one year listings. That is, a category of listings coming on the market is tracked. Those that sell within a year of entering the market are compared with the entire listing population. High percentages are indicators of a seller’s market, and low percentages for a buyer’s market. Sales Volume: The dollar amount of a quantity of sales during some given time interval. Sample: A subset of a population. A meaningful sample reflective of the population must be randomly chosen from within the population. Sampling itself, is a science and an art. Scale: In a graph, a visual relationship between a distance and a numerical magnitude. Script: An outline of “patter” used in sales training to demonstrate a possible conversation between a agent and a customer or client. Not to be memorized or followed exactly. Used to show important points, and suggested “flow” of conversation. Seasonal Index: A series of numbers representing the seasonal fluctuations in a time series. The curve of the index points can be considered the slope of the seasonal trend and used to remove the trend from a composite graph. See Also: Time Series Analysis Seasonal Trends: (Seasonal pattern, seasonal factors, seasonally adjusted). Plotting data over a time scale, (such as annual sales), can reveal the same cycle or pattern occurring at the same time in the overall data set. Often these increases or decreases can be attributed to seasonality- cyclic buying habit repeated annually. When a graph of sales is being decomposed into various contributing factors, the seasonality is subtracted out to show the true increase or decrease in the month to month volume of sales. Seller: The future grantor of the deed in a real estate transaction. One receiving an offer to purchase real estate. One who has title to property. Seller’s Market: A term referring to an advantage the seller has in negotiating an offer. Seller’s Market can refer to a general region, or a narrow category of the entire market. For the most part, a seller’s market is the opposite of a Buyer’s Market. Evaluating a buyer or seller’s market involves three elements: 1. How many homes that are listed in the given category will actually sell? (In a Seller’s Market the higher the percentage, the stronger the seller’s market.) 2. How fast are the homes selling? (The shorter the “days on market” (DOM), the better for the seller.) 3. What is the “sales to list price ratio?” (The higher the percentage, the better for the seller.) All these elements can be combined in a general formula. The more independent of each other are the elements, the better the resulting formula. The result of the formula is a relative number and has no absolute standard by which to be measured. However, in time an index can be established and a maximum and minimum figure used to gage whether an existing market is either a buyer or seller’s market. Seller’s Net Proceeds Sheet: A list of all the cost and fees, including commission, paid by the seller at the closing. Has a final “Walk-away” amount for the seller, listed at the bottom. Series: A collection, group or
set of values or data points that are related to each
other. Significant: A term used in statistics meaning the results were not due to random factors alone and therefore must be considered. Skew: A descriptive term indicating lopsidedness in a number distribution. Compare to symmetrical. A positive skew produces a graph with most of the data points to the left of the mean. In a negative skew they lie to the right. Slope: Generally meaning a measure of the steepness of a curve. With a straight line graph, the slope remains constant throughout the range of the graph. Most curves show a changing slope at every data point. Slopes can range from -µ to 0 to +µ. A positive slope indicates a rising curve, negative slopes-a falling curve. For a straight line curve only two points are needed to determine the slope. Dividing the difference of the dependent variables by the difference of the independent variables will give the slope. A slope of 0 is a horizontal line. Infinite slope is a vertical line. Calculating the slopes for most curves requires calculus. Example: The slope of a normal sine-wave starts (y = Sin(X) the beginning data point being X=0, Y=0) at a slope of 1 decreases steadily to 0 at the maximum part of the curve (X = 900), continues to decrease and crosses the Y=0 point with a slope of –1, (X = 1800), then increases its slope again to 0 at the minimum value (X=2700), and continues to increase reaching a slope of 1 once again at the beginning of the cycle. See Also: Graphs, Time Series Analysis Source of Buyers: Used as a graphic to show the seller the resources of the company or the agent for procuring buyers. Often explained as the different buyer “streams” that go to make up the Buying Pool. Speculation: The attempt to read the future demand of a product or service and to invest ones capital in it, hoping to make a profit. Spread: The range of values in a distribution. Meant to convey variability and dispersion. Spurious: Not genuine, true or authentic. Coming from a wrong source. In statistics usually applied to data points indicating some of the data is made-up, from an incorrect source, or is somehow misrepresented. Square Footage: A measurement of area in a dwelling unit. Found by dividing the area of a unit into non-overlapping rectangles and multiplying the length by the width, then summing all the rectangles. Stable: Or Stable Market. A relative term describing the midpoint between two extremes. It usually implies an “unchanging” or non-volatile condition, but can also indicate a place of “equilibrium” and relatively quiet activity. Example: When compared to a Seller Market, or Buyer’s Market, a Stable Market would be one that has no advantage to either the buyer or seller. A “neutral” zone so to speak. Standard: An absolute or acceptable reference by means of which other elements can be judged or evaluated. Example: if 9 rooms is the standard for homes in a subdivision, we can now judge a home with 7 homes to be below standard, and one with 11 as being above standard. Standard Deviation: Calculated by means of a statistical formula and used to report the average change of a series of numbers. Static Chart or Graph: One in which current market conditions do little to change its essential message. A Time Vs. List to Sales Price Ratio Chart would be an example. See Also: Dynamic Chart or Graph Statistician: One engaged in statistical research. Statistic: Characteristics or facts about a given sample. See Also: Parameter and Population Statistics: A branch of science dealing with the distribution, analysis, and forecasting techniques of various number series. Subdivision: An area of a community characterized by similar homes as to square footage, age, and style; all platted at the same time and called a specific name. Subdivision Developer: See Developer. Subjective: Arising from the needs, desires, or perceptions of one individual, and not necessarily applicable to universal verification. Supply: The idea of supply and demand is central to any discussion of the exchange of goods and services. In relation to real estate, supply is the inventory of homes on the market at any given moment. (current listings also called the listing pool). Many factors can add to the supply of homes coming on the market. The amount of new homes especially, is connected with interest rates . The employment market also factors in to new construction, thus increasing the supply. Other factors affecting supply are: owners wanting to downsize or move up; industrial lay-offs; job transfers and profit taking. Survey: In real estate, a diagram showing the boundary points and easements connected with property. In statistics, obtaining data from a subgroup in an effort to draw conclusions about the entire group. See Also: Random, Interpretation Symmetrical: Indicates a graph that reflects a mirror image around either a vertical or horizontal line. (Or both.) |
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Table: A method of displaying data using columns and rows rather than visual elements. Time Series: A series of data points that represent independent variables measured over equal time intervals and the resulting dependent variables they generate. Example: a twelve month series of sales volume for a particular area would be a time series. The monthly intervals are of equal time frames and the volume of sales would be considered the dependent variables. Time Series Analysis: The study, description and analysis of a time series. Time series graphs are often composite graphs which can be broken down into component graphs. These include: the trend, the seasonal factors, and the business cycle. The remaining data point residuals should form a random scattering of points indicating no other patterns or trends are present. Title Company: An insurance company issuing a policy that protects a buyer from defects in the public records, and other types faulty documents, which could challenge the ownership of the property. Total: In this context it means both existing and new construction markets. Transaction: The sale of a piece of property. There are two sides to a transaction. The listing company and the selling company. Both can use the full sale price for purposes of reporting their volume of business. Track: To follow a series of events looking for patterns or key indicators. In real estate statistical analysis, we track many different time series events, such as: sales, pending, inventory, agent productivity plus scores more. Transaction: A term meaning the transfer of property between a seller and a buyer Trend: Establishing a rising or falling curve for graphed data points presented over a time series. Trend lines indicate the general “slope” of the given graph. Useful in business planning and forecasting techniques. Trend lines are generally considered “straight” lines. This is a misconception. Although straight lines are useful for short term forecasting, other trend lines, such as exponential, logarithmic, and moving-averages are possible and often give better results. Trough: The lowest point in the Business Cycle. See Also: Business Cycles, Depression, Economic Indicators, Gross Domestic Product, Recession, Peak True Available Inventory (TAI): Reporting all listings that were current at a particular time in market history. Can be calculated long after the present date. |
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Under Contract: A term used in real estate to indicate there is a contract on the home and a closing date has been set. Unemployment Index: One of the primary indicators of economic health of a nation or a local area. Usually reported as a percentage of the work force that is not working (of all those who wish to be,) at the time of inquiry. Even though a full work force is an ideal, and considered good, it does have downsides. Employers find it more difficult to fill positions as the unemployment rate shrinks. This often leads to hiring unqualified or disinterested employees. Customer service may suffer. Units: Members of any population considered as individuals. Units are counted to arrive at a sum. Units Sold: The amount of sales as opposed to the volume of sales of real estate property. Unmotivated Seller: A seller lacking any time constraints for selling his homes. Time constraints make the seller flexible to current market conditions,. Lack of time constraints tend to make sellers, unrealistic and demanding. US Census: A periodic sampling of
the entire population of the
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Value: The perceived worth of an object, or the present worth of future benefits. Variability: A measure of how much spread a data set contains. Meant to convey dispersion and scatter. Variable: A
quantity or attribute that can change; either over time or by some other
factor. Visuals: Charts, graphs, or graphics used in a presentation to reinforce your words, and act as a point of focus for the clients. See Also: Presentation Volatility: The suddenness of changing conditions. We speak as “Volatile” those events or elements of a situation that are subject to a high degree and speed of change. Includes a feeling of being unpredictable. Example: in real estate, the change in he amount of the listings for any given city and price category is much more volatile than the change in amount of listings for the entire region. A volatile chart is one in which there are wide swings in amplitude of the graph from the reference or zero point. Compare with its opposite: stability. |
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Walk-away Price: What a seller can expect as their net income at the closing table. See Also: Net Proceeds of Sale Weighted Average: A weighted average is when one of the data points in a series is counted more than once, or is increased by a certain percentage because of its significance. Example: suppose an appraiser values a piece of property at $86,000 as a single-family residence and at $89,000 as a rental home. To report his final appraisal, he may merely take the mean of the two values: $86,000 + $89,000 = 175,000/2= $87,500. However, suppose he believes that the rental value is more reflective of the neighborhood. He may decide to “weight” the rental value more than the single-family value. Say he decides that the rental value should be 60% of the whole, and the single-family 40% then: ($86,000*.4 +$89,000*.6)=$87,800. Rationale: sometimes certain data points may be deemed more significant that others. In this case weighing the significant points above those less significant will give an average more in keeping with the real world. Uses: combining two or more averages often demands the use of weighted averages. Example: the mean of one series is 12 and the mean of another is 14 the simple mean of the two (12+14)/2=13 may work as long as the same amount of data points or elements are in each series. But suppose the series with mean = 12 has 6 elements and the series mean = 14 has 3 elements. Then the weighted average would be: (12*6+14*3)/9=12.67, which is the same result if we combined all data points from both series and then took the mean. See Also: Central Location Withdrawn: A listing that is removed from the market before its expiration date is reached. |
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